How fast would a 60cm diameter ball of glass be falling?

Question

at 1m above ground, if it had been droped from 50000 feet,and what would its max speed be? and what if you could drop it in a vacum from the same hight what would be the difference?

Answer 1

If you drop it in a vacuum and towards the Earth, it wil start falling from 0m/s and accelerate by 9.81m/s.
Its speed after a time will be v = a.t = 9.81 * t.
For a given distance, the formula e = (a*t^2)/2, where e is the distance in meters, a=9.81m/s^2 and t the time in seconds.
Use the two formulas to find the final speed.
If you drop it TRHOUGH the air, the ball is submitted to TWO forces: the earth attraction, which is constant, and the AIR RESISTANCE, that increase to the square of the speed of the ball.
When the two forces are equal (the force of gravitation and the force of air resistance), the ball will have reached its "terminal velocity".
Just have to get details of air resistance, now.
This depends of the projected surface of the ball (its diameter), its shape, the density of the air and, finally, the relative speed of the ball through the air.
Samurai: 245 kph is the average terminal velocity of a human being doing a free fall from 12,000 feet, and falling flat on his belly. This reaches 275 kph if the freefaller plunges head first, arms against the body. You got your data from the movie...

Answer 2

The air resistance is
6 pi eta v r
where eta=1.8E-5 Ns/m^2 is air's viscocity, v is the speed and r is the radius of the ball. So the maxium speed is
mg/(6 pi eta r)
where
m=4/3 pi r^3 rho
where rho is the density of glass, typically 2600 kg/m^3
now google on
4/3 * pi * (30 centimeters)^3 * (2600 kilograms per cubic meter) * 1 (9.82 meters per square second) /(6 *pi * 0.000018 Newton seconds per square meter* 30 centimeter)
and you get
28 368 888.9 m/s

which is such an incredible high speed that air resistance is probably irrelevant for your purpose. You might as well assume that the ball is in a vacuum and trust the results posted by others.

Answer 3

The terminal velocity in a vacuum would be √(2gh) where h is height in meters and g = 9.8 m/s² Conver the 50000 feet to meters (15245) and subtract 1 (for the speed at 1 meter above the ground) to get
√(2*9.8*15244) = 546.6 m/s

Air resistance is a fairly complex thing. The sphere would be going slower if there were air present, but I have no idea how to go about calculating it.


Doug

Answer 4

i think terminal velocity on earth is 9.8mps (or something near that), nothing would ever really reach that speed though because of wind resistence. If earth somehow didnt have an atmosphere then it would get to terminal velocity and like the experiment on the moon with the feather and the hammer without an atmosphere the shape/size/mass of the object will make no difference to how fast it falls

Answer 5

In a vacuum, the ball's final velocity would be 547 m/s. We know this because of equations that we can derive from Galileo's kinematics equations. Namely the equation for time independant acceleration is:

Vf^2 - Vo^2 = 2AD

Vf is final velocity, Vo is original velocity, A is constant acceleration, and D is displacement (the distance which the object moved).

If we read the equation out loud we would say:
"Final velocity squared minus original velocity squared is equal to two times the acceleration times the displacement."

If we want to solve for final velocity, we can isolate it by adding Vo^2 to both sides of the equation:
Vf^2 = 2AD + Vo^2

Now we just need to plug in some numbers. The ball isn't moving before we drop it, so it's original velocity is zero (Vo = 0). Acceleration due to gravity is constant. On earth, all objects accelerate at 9.81 meters per second per second (A = 9.81 m/s^2). The displacement is how far the ball moved. If we're looking at one meter above ground, it would have moved 15,239 meters (one foot is equal to 0.3048 meters), so (D = 15,239). Now we have an equation we can solve:
Vf^2 = 2AD + Vo^2
-----substitute known values---
Vf^2 = (2 * 9.81 * 15,239) + 0^2
----simplify terms---
Vf^2 = 298989.2 + 0
----take the square root of each side to get (Vf)---
Vf = 546.8 m/s (about 1,223 mph)

Hope that helped.

Answer 6

if in a vacume it would fall at the rate of gravity on earth i think its bout 10mps^2 not sure bout its terminal velocity tho :(

Answer 7

Terminal velocity 245kmph
in vacuum conctantly accelerate at 10m/s/s

Answer 8

everthing falls at the same speed it called gavatiy, 1kg of feathers falls the same speed as 1kg of lead

Answer 9

is the ball hollow or solid

Answer 10

Jesus thats one for mastermind?